Pressure Distributions

In the cylindrical portion of a hopper the pressure distribution can be derived if the following assumptions are made  

The vertical compressive stress is constant over any horizontal plane. 

The ratio of horizontal and vertical stresses is constant and independent of depth. 

The wall friction is fully mobilized, meaning that the particulate material is in incipient slip conditions at the wall. 

A force balance over a differential element (see Fig. 7.7) gives  

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Introduction and Commercial Application Section 8.0 considered the dynamic behaviour in the reservoir, away from the influence of the wells. However, when the fluid flow comes under the influence of the pressure drop near the wellbore, the displacement may be altered by the local pressure distribution, giving rise to coning or cusping. These effects may encourage the production of unwanted fluids (e.g. water or gas instead of oil), and must be understood so that their negative input can be minimised. 

Step 4 - it is initially assumed that the flow field in the entire domain is incompressible and using the initial and boundary conditions the corresponding flow equations are solved to obtain the velocity and pressure distributions. Values of the material parameters at different regions of the domain are found via Equation (3.70) using the pseudo-density method described in Chapter 3, Section 5.1. 

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

Fluid-pressure distribution tends to close the valve. For this reason, the smaller manually operated valves have a latching device on the handle, and the larger manually operated valves use worm gearing on the stem. This hydraulic unb ance is proportional to the pressure drop and, with line velocities exceeding 7.6 m/s (25 ft/s), is the principal component in the torque required to operate the valves. Compared with other valves for low-pressure drops, these valves can be operated by smaller hydrauhc cylinders. In this service butterfly valves with insert bodies for bolting between existing flanges with bolts that... 

For incompressible cake, the pressure distribution and the rate depend on the resistance of the filter medium and the permeability of the cake. Figure L8-150 shows several possible pressure profiles in the cake with increasing filtration rates through the cake. It is assumed that r /i i = 0.8 and /p//i = 0.6. The pressure at / = ri, corresponds to pressure drop across the filter medium Ap, with the ambient pressure taken to be zero. The filtration rate as well as the pressure distribution depend on the medium resistance and that of the cake. High medium resistance or blinding of the medium results in greater penalty on filtration rate. 

FIG. 29-29 Velocity and pressure distribution in a three-stage reaction turbine. 

Turbomaehinery bearing systems are normally designed for radial loads eorresponding to the weight of the rotor. Non-uniform pressure distribution around the wheel(s) of a turbomaehine may also eontri-bute to the magnitude of gas dynamie radial load, oeeasionally ealled side load. The sourees of gas dynamie radial loads on the eom-pressor wheel are different from those at the expander wheel. 

On the expander side, the expander wheel is surrounded by the nozzle vanes. The nozzle vanes, in turn, reeeive gas from a toroidal spaee that is eonneeted to tlie expander inlet piping. Any non-uniformity in the torus spaee and/or in the nozzle vane design may result in a non-uniform pressure distribution around the expander wheel. Non-uniform gas pressure around the expander wheel will result in a non-uniform load and, henee, produee a gas dynamie radial load on the bearing. In the expander ease, however, the nozzle throat flow resistanee is mueh larger than the easing peripheral pressure nonuniformity. The latter aets as a buffer making the expander wheel eireumferential pressure variations smaller than those of the eompressor side. This smaller pressure variation produees mueh less radial load when eompared to that of the eompressor side. 

NACA has given design points for eaeh easeade tested. Eaeh design point is ehosen on the basis of the smoothest pressure distribution observed on the blade surfaees if the pressure distribution is smooth at one partieular ineidenee at low speed, it is probable that the seetion will operate effieiently... 

EXTERNALLY SUPPLIED MYOROSTATIC FLUID PRESSURE DISTRIBUTION... 

Build-up of solids in rotor andjor stator pas.sages ( plugging of turbine buckets). This problem should be notieed from performanee or pressure distribution in the maehine (first-stage pressure) long before the failure oeeurs. 

Whereas the JKR model approached the topic of particle adhesion from a contact mechanics viewpoint, the DMT theory simply assumes that the adhesion-induced contact has the same shape as a Hertzian indentor. The normal pressure distribution Ph(p) for the Hertzian indentor is related to the repulsive force and the distance from the center of the contact circle to the point represented by r according to the relationship [49]... 

FIGURE 7.101 Pressure distribution doe to wind effect o) uniform wind velocity profile (6) non-uniform wind velocity profile. 

FIGURE 7.103 Pressure distribution inside and outside a building with a single large opening. 

Swann, M. V., and S. Chandra. 1988. Correlations for pressure distribution on building.s and calculation of natural-ventilation airflow. ASHRAE Transactions, vol. 94, no. 1, pp. 243-266. 

When designing air supply through a filter ceiling, one should ensure that the dynamic pressure in the supply air does not affect the static pressure distribution above the filter ceiling too much. 

Perforated sheets are, however, much more vulnerable to uneven pressure distributions and tilted inflow of air, as illustrated in Fig, 8,26. The supply air entering horizontally alxive the perforated sheet partly maintains its horizontal velocity component when being discharged through the holes in the perforated sheet. Thus, it leaves the perforated sheet at an angle less than 90°. The suction between the small outflowing jets also makes the airflow stick to the perforated sheet and flow along the sheet instead of perpendicular to (t. 

FIGURE 8.26 The outflow from perforated sheets is vulnerable to tilted inflow and to uneven pressure distribution. 

Iversen, H. W., Rolling, R. E., Carlson, J. J. Volute pressure distribution, radial force on the impeller and volute mixing losses of a radial flow centrifugal pump. Trans. ASME, journal of Engineering for Tower 82 (1.960), pp. 136-144. 

Wind pressure distribution Set of wind pressure coefficient data for each external node... 

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